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BHOoi16-Pearl
16-Pearl
October 7, 2016
Question

How to create evenly distributed points on a sphere?

  • October 7, 2016
  • 10 replies
  • 12197 views

A very simple problem but i failed to figure it out.

Is there an easy way to create the points? Any suggestions/tricks? Thanks

    10 replies

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    TobiasLarsson12-Amethyst
    12-Amethyst
    October 7, 2016

    Could this help?

    Reg: creating a pattern in sphere

    Help in golf ball modelling

    GOLF - Gentleman Only, Ladies Forbidden?

    //Tobias

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    BHOoi16-PearlAuthor
    16-Pearl
    October 7, 2016

    wow, none looks simple and some are not evenly spaced. Good reference anyway, thanks. Those were about 3 years ago, hopefully Creo is more capable now

    D
    dschenken1-Visitor
    1-Visitor
    October 8, 2016

    I searched Google for "points evenly spaced on sphere" and got this: Distributing points on the sphere | School of Mathematics and Statistics which mentions "it is not possible to equally distribute points on the sphere except in a few special cases"

    It's a difficult problem for anything not trivial. It does not surprise me that Creo does not address this.

    B
    BHOoi16-PearlAuthor
    16-Pearl
    October 10, 2016

    I have tried patterning but it's still pretty manual. I don't have any image, and just thought of creating something similar to a golf ball.

    B
    BHOoi16-PearlAuthor
    16-Pearl
    October 10, 2016

    I got this link from PTC's reply, but still have no clue how to creat it

    https://support.ptc.com/appserver/cs/view/solution.jsp?n=CS177218&lang=en_US

    Patriot_1776
    Patriot_177622-Sapphire II
    22-Sapphire II
    October 11, 2016

    Pshaw, that's easy.....I just put one point at the North pole, and one at the South pole (2 "points" total), exactly per your request, done! 

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      BHOoi16-PearlAuthor
      16-Pearl
      October 12, 2016

      Capture.JPG

      B
      BHOoi16-PearlAuthor
      16-Pearl
      October 12, 2016

      I found a page below:

      How can I generate uniformly spaced points on the surface of a sphere? - Quora

      and i ended up with:

      Capture.JPG

        Patriot_1776
        Patriot_177622-Sapphire II
        22-Sapphire II
        October 13, 2016

        Actually, I never got to play around with making a golf ball, but, this is exactly what I was thinking I would try.  Since a sphere can be divided up into equal triangular facets, I figured an approach like this would work.  Nice find!

        H
        HarikrishnanR1-Visitor
        1-Visitor
        October 12, 2016

        GOLF - Gentleman Only, Ladies Forbidden? - PTC Community-  Vladimir Palffy

        -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

        Thanks

        Hari

        “Share your knowledge. It is a way to achieve immortality.” - Dalai Lama.

        B
        BHOoi16-PearlAuthor
        16-Pearl
        October 14, 2016

        This is how I construted the edges of the trinagle of regular icosahedron.

        Capture.JPG

        B
        BHOoi16-PearlAuthor
        16-Pearl
        October 14, 2016

        another approach:

        Capture.JPG

        K
        Kevin1-Visitor
        1-Visitor
        October 14, 2016

        Wiki has info that talks point distances relate to the radius of a sphere. The simplest approach for the icosahedron that I found is to create a sketch with the diameter desired, create a line that goes through the center with the ends on the circle, place points on each end of the line since the points will alternate from northern to southern hemisphere, write a relation for the angle of the line from the latitudinal plane of arctan(.5), pattern the sketch about the longitudinal axis with a spacing of 5 element within 360 degrees, and the final two points are at the north and south poles of the sphere.

        T
        TomD.inPDX17-Peridot
        17-Peridot
        October 15, 2016

        Have you tried the fill pattern's advanced features?

        K
        Kevin1-Visitor
        1-Visitor
        October 16, 2016

        ‌I took a look at this but based on what I'm seeing although it will get points on the spheres surface it can't duplicate the method used to create the points. The most appropriate would be to pattern the points on a sketched curve but the projections or mappings of the points to the surface are off. From what I can see the pattern options can't handle the radial projection of the individual points which is required to get the points in the right places.

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        bnielsen-21-Visitor
        1-Visitor
        October 20, 2016

        Hi @BH001,

        It looks like you've gotten a lot of responses already, but I thought I'd add my $0.02:

        After skimming through the various responses, I saw that someone did effectively answer [correctly]: it's not possible to distribute N points on a sphere with perfectly even spacing between adjacent points when N is above a certain number (I'm not certain, but I seem to remember number N=20 for some reason.  I wouldn't swear to this though).

        However, this is an active problem in mathematics; please refer to this PDF of a relatively rigorous analysis of the problem: https://perswww.kuleuven.be/~u0017946/publications/Papers97/art97a-Saff-Kuijlaars-MI/Saff-Kuijlaars-MathIntel97.pdf

        Also, I didn't see it in that PDF but I distinctly remember reading about fibonacci arrangements of pollen as well, something that was studied in the first half of the 20th century by a well-known biologist (whose name also escapes me, of course).  I think this is the relevant paper: https://arxiv.org/pdf/0912.4540.pdf

        Also, these links may be of some help as well:

        http://stackoverflow.com/questions/9600801/evenly-distributing-n-points-on-a-sphere

        https://my.vanderbilt.edu/edsaff/spheres-manifolds/

        Please let us know how your research goes and what you decide on doing!

          B
          BHOoi16-PearlAuthor
          16-Pearl
          October 21, 2016

          Thanks for those links, Ben. I will spend some time going through them but I doubt i will be able to understand them all .

          So far, the best solution is still through icosahedron but it has limited number of points and further splitting is pretty a tedious task.

          T
          TomD.inPDX17-Peridot
          17-Peridot
          October 21, 2016

          Something to consider is building 1 quadrant and learn how to use the transformation matrix.  When I was doing the Golf Ball, everything could be mirrored X and Y, then transform the set of 4, twice.

          The subdivision is the one thing that there has to be a better way.  You do know you can use polar coordinate systems, right?

          Is there an advantage there?

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